Beschreibung
Extracting precise cosmological constraints from cosmic shear observations requires accurate modeling of the non-linear matter power spectrum, which is suppressed at small scales ($k\sim$1 to 10$\,h~$Mpc$^{-1}$) due to baryonic feedback. Various hydrodynamical simulations predict different levels of matter power spectrum suppression based on the type and strength of the feedback mechanisms employed. The intracluster medium (ICM) mass in galaxy clusters is strongly correlated with the cluster halo mass, and this relation -- especially the mass dependence of the relation -- is sensitive to baryonic feedback processes. While the measurement of ICM masses M_ICM within a specified radius has long been routine using X-ray observations, the extraction of robust cluster halo masses and their uncertainties using survey weak lensing datasets is relatively new. We constrain the M_ICM-M_500c-z relation using 122 South Pole Telescope thermal Sunyaev-Zel'dovich effect (tSZE) selected galaxy clusters with M_ICM measurements based on deep observations with the Chandra X-ray Observatory and \textit{XMM-Newton}, along with newly calibrated halo masses M_500c derived using weak gravitational lensing data from the Dark Energy Survey. By comparing the observed cluster relation with the relation extracted from a variety of hydrodynamical simulations that incorporate a range of feedback models, we extract a marginal likelihood for each simulation. We use these marginal likelihoods, together with the matter power spectrum from each simulation, to infer the baryon-suppressed matter power spectrum and its 68\% credible interval. This methodology allows us to rule out some extreme feedback scenarios that include too much or too little feedback. Furthermore, we investigate the cosmological dependence of this suppression, finding it to be primarily sensitive to the cosmic baryon fraction, while the residual dependence on $\Omega_{\mathrm{m}}$ and $\sigma_8$ at fixed baryon fraction remains sub-dominant and at the percent level. These findings suggest that baryonic suppression alone may not be sufficient to reconcile the differences between cosmological parameters from $z\lesssim1$ cosmic shear and Planck primary CMB analyses. This approach underscores the usefulness of well-defined tSZE-selected galaxy cluster samples with associated deep X-ray observations and survey weak lensing data for constraining baryonic feedback, and thereby better defining the matter power spectrum at small scales. These results and future analyses with larger samples and improved weak lensing datasets will be essential for obtaining unbiased cosmological constraints and improving our understanding of dark matter with future cosmic shear experiments like those planned with the Euclid mission and the Rubin Observatory.